What major "army" rose up against Lenin's Red Army?

The "White Army" or "the White Guard."

Explanation

It was a counterrevolutionary army that was made by units and headed by some top oficcers of the former czarist army such as Gen. Kornilov and Gen. Denikin.

Its objective was to topple the Bolshevik government and denounce the Treaty of Brest-Litovsk (1918), which had made enormous territorial concessions to Germany and had taken Russia out of WWI. The White Army was supported by the Western Powers because they were interested in re-establishing the Eastern Front. Its disappearence had allowed Germany to redeploy more armies in the Western Front, increasing its might.

The White Army

Explanation:

The Red Army-backed by Lenin's newly formed Russian Communist Party-fought the White Army, a loose coalition of monarchists, capitalists and supporters of democratic socialism.